A convergence criterion for real Fourier series, which is based solely
on the behavior of the Fourier coefficients, is proposed and
demonstrated in a simple case. The proof of convergence is based on a
geometrical construction on the complex plane, and can be understood as
an application of the Dirichlet convergence test. The class of
convergent Fourier series thus defined is then extended to several other
cases. The possible algorithmic applications of the result are pointed
out, and the analytical character of the resulting set of limiting
functions is briefly commented on.

- Introduction
- Geometrical Representation on the Complex Plane
- Proof of a Simple Convergence Theorem
- Rigorous Proof of the Theorem
- Extension of the Result to Other Cases
- Possible Algorithmic Applications
- Analytical Character of the Limits
- Final Comments
- Bibliography